Induced Topological Terms, Hidden Local Symmetry, and Anyon Superconductivity

1991 ◽  
Vol 05 (10) ◽  
pp. 1763-1770 ◽  
Author(s):  
C.-L. Ho ◽  
B. Hu ◽  
H. L. Yu
Keyword(s):  
Particle Physics ◽  
Quantum Fluctuations ◽  
Local Symmetry ◽  
Three Dimensions ◽  
Direct Connection ◽  
Fractional Statistics ◽  
Four Dimensions ◽  
Chern Simons ◽  
Natural Way

We show how the topological Chern-Simons term in three dimensions and the θ-term, [Formula: see text] in four dimensions can be dynamically generated due to quantum fluctuations in Nambu-Jona-Lasinio models. These results give a vivid demonstration of hidden local symmetry at work. The fluctuation-induced Chern-Simons term provides a natural way to incorporate fractional statistics and thus a more direct connection with anyon superconductivity. Possible phenomenological implications of this approach in particle physics are also discussed.

VECTOR PAIRING AND FLUCTUATION-INDUCED CHERN-SIMONS TERM IN ANYON SUPERCONDUCTIVITY

1990 ◽  
Vol 04 (18) ◽  
pp. 1137-1141 ◽  
Author(s):  
CHOON-LIN HO ◽  
BAMBI HU ◽  
HOI-LAI YU
Keyword(s):  
High Temperature ◽  
High Temperature Superconductivity ◽  
Quantum Fluctuations ◽  
Direct Connection ◽  
Fractional Statistics ◽  
Fermion Model ◽  
Chern Simons ◽  
Natural Way

Assuming some sorts of vector pairing in high-temperature superconductivity, we show how the topological Chern-Simons term can be generated dynamically due to quantum fluctuations in a BCS-type four-fermion model. This fluctuation-induced Chern-Simons term provides a natural way to incorporate fractional statistics and thus a more direct connection with anyon superconductivity.

scholarly journals Skyrmions, Quantum Hall Droplets, and one current to rule them all

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Avner Karasik
Keyword(s):  
Vector Fields ◽  
Quantum Hall ◽  
Local Symmetry ◽  
Effective Theory ◽  
Vector Mesons ◽  
Low Energies ◽  
Baryon Current ◽  
Chern Simons ◽  
Natural Way

We introduce a novel Skyrme-like conserved current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The associated charge is equivalent to the skyrmion charge for any smooth configuration. In addition, there exist singular configurations that can be identified as N_f=1Nf=1 baryons charged under the new symmetry. Under this identification, the vector mesons play the role of the Chern-Simons vector fields living on the quantum Hall droplet that forms the N_f=1Nf=1 baryon. We propose that this current is the correct effective expression for the baryon current at low energies. This proposal gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. In addition, Chern-Simons dualities on the droplet can be interpreted as a result of Seiberg-like duality between gluons and vector mesons.

N=2 SUPERSTRING THEORY GENERATES SUPERSYMMETRIC CHERN-SIMONS THEORIES

1994 ◽  
Vol 09 (35) ◽  
pp. 3255-3266 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Integrable Models ◽  
Three Dimensions ◽  
Superstring Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Fundamental Significance ◽  
Background Fields ◽  
Chern Simons

We show that the action of self-dual supersymmetric Yang-Mills theory in four dimensions, which describes the consistent massless background fields for N=2 superstring, generates the actions for N=1 and N=2 supersymmetric non-Abelian Chern-Simons theories in three dimensions after some dimensional reductions. Since the latters play important roles for supersymmetric integrable models, this result indicates the fundamental significance of the N=2 superstring theory controlling (possibly all) supersymmetric integrable models in lower dimensions.

scholarly journals Compactifying 5d superconformal field theories to 3d

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Matteo Sacchi ◽  
Orr Sela ◽  
Gabi Zafrir
Keyword(s):  
Riemann Surfaces ◽  
Recent Progress ◽  
Three Dimensions ◽  
Field Theories ◽  
Global Symmetry ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
The One ◽  
Conformal Manifolds ◽  
Chern Simons

Abstract Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d$$ \mathcal{N} $$ N = 1 theories, we initiate a systematic study of compactifications of 5d$$ \mathcal{N} $$ N = 1 SCFTs on Riemann surfaces to 3d$$ \mathcal{N} $$ N = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg $$ {E}_{N_f+1} $$ E N f + 1 SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.

scholarly journals Witten effect, anomaly inflow, and charge teleportation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hajime Fukuda ◽  
Kazuya Yonekura
Keyword(s):  
Quantum Mechanics ◽  
Magnetic Monopole ◽  
Charged Particles ◽  
Magnetic Monopoles ◽  
Three Dimensions ◽  
Total Charge ◽  
Four Dimensions ◽  
Linking Number ◽  
M Theory ◽  
Chern Simons

Abstract We study a phenomenon that electric charges are “teleported” between two spatially separated objects without exchanging charged particles at all. For example, this phenomenon happens between a magnetic monopole and an axion string in four dimensions, two vortices in three dimensions, and two M5-branes in M-theory in which M2-charges are teleported. This is realized by anomaly inflow into these objects in the presence of cubic Chern-Simons terms. In particular, the Witten effect on magnetic monopoles can be understood as a general consequence of anomaly inflow, which implies that some anomalous quantum mechanics must live on them. Charge violation occurs in the anomalous theories living on these objects, but it happens in such a way that the total charge is conserved between the two spatially separated objects. We derive a formula for the amount of the charge which is teleported between the two objects in terms of the linking number of their world volumes in spacetime.

scholarly journals Effective theories and non-minimal couplings in low-dimensional systems

2021 ◽  
pp. 2150099
Author(s):  
M. G. Campos ◽  
L. P. R. Ospedal
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Minimal Coupling ◽  
Four Dimensions ◽  
Dimensional Spacetime ◽  
External Electromagnetic Fields ◽  
Fermionic Fields ◽  
Low Dimensional ◽  
Effective Theories ◽  
Chern Simons

Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy–Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields. Next, we establish some comparisons and analyze particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell–Chern–Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.

scholarly journals 𝒩 = 2 dualities and Z-extremization in three dimensions

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Brian Willett ◽  
Itamar Yaakov
Keyword(s):  
Three Dimensions ◽  
Partition Functions ◽  
Recent Proposal ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
Seiberg Duality ◽  
Real Mass ◽  
Supersymmetric Gauge ◽  
Chern Simons

Abstract We use localization techniques to study duality in 𝒩 = 2 supersymmetric gauge theories in three dimensions. Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms. These theories have the possibility of non trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine. We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms. The results provide strong evidence for the validity of the proposed dualities. We also comment on a recent proposal for recovering the exact IR conformal dimensions in such theories using localization.

scholarly journals LARGE QUANTUM GRAVITY EFFECTS: CYLINDRICAL WAVES IN FOUR DIMENSIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 669-686 ◽  
Author(s):  
MARÍA E. ANGULO ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Quantum Gravity ◽  
Symmetry Axis ◽  
Point Of View ◽  
Three Dimensions ◽  
Asymptotic Region ◽  
Four Dimensions ◽  
Cylindrical Waves ◽  
Significant Difference ◽  
Gravity Effects ◽  
Linearly Polarized

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein–Gordon) field in three dimensions. The quantization of this latter system was performed by Ashtekar and Pierri in a recent work. Employing that quantization, we obtain here a complete quantum theory which describes the four-dimensional geometry of the Einstein–Rosen waves. In particular, we construct regularized operators to represent the metric. It is shown that the results achieved by Ashtekar about the existence of important quantum gravity effects in the Einstein–Maxwell system at large distances from the symmetry axis continue to be valid from a four-dimensional point of view. The only significant difference is that, in order to admit an approximate classical description in the asymptotic region, states that are coherent in the Maxwell field need not contain a large number of photons anymore. We also analyze the metric fluctuations on the symmetry axis and argue that they are generally relevant for all of the coherent states.

On Five Lines, in Space of Four Dimensions, which lie upon a, Quadric Threefold and the Normal Quartic Curves of which they are Chords

1924 ◽  
Vol 22 (2) ◽  
pp. 189-199
Author(s):  
F. Bath
Keyword(s):  
Three Dimensions ◽  
Apparent Contradiction ◽  
Four Dimensions ◽  
Quartic Curve ◽  
Lines In Space ◽  
Quadric Threefold ◽  
Quartic Curves

The connexion between the conditions for five lines of S4(i) to lie upon a quadric threefold,and (ii) to be chords of a normal quartic curve,leads to an apparent contradiction. This difficulty is explained in the first paragraph below and, subsequently, two investigations are given of which the first uses, mainly, properties of space of three dimensions.

THE PAULI TERM AS A GENERATOR OF FRACTIONAL SPIN

2011 ◽  
Vol 26 (19) ◽  
pp. 1427-1432
Author(s):  
J. S. N. FURTADO ◽  
F. A. S. NOBRE
Keyword(s):  
Fractional Statistics ◽  
Fractional Spin ◽  
Chern Simons ◽  
Matter Fields

In this work, we show that contrary to what is commonly accepted by the community, the Chern–Simons term is not essential to fractional statistics. A Lagrangian whose dynamics is governed only by the Pauli term coupled to matter fields leads to the fractional spin. Despite its simplicity, development of this Lagrangian gives rise to essentially the same terms that appear in Chern–Simons models, such as those reported by Nobre and Almeida.13,8,9

Sign in / Sign up

Export Citation Format

Share Document